# The Higgs Story-Part 12: How the quarks and leptons acquire masses

In the previous post in this series, we saw how the Higgs mechanism gave rise to the masses of the weak interaction force particles W+, W, and Z. We also saw how the process of spontaneous symmetry breaking that was part of that mechanism resulted in the Higgs field having a non-zero average value even in the vacuum, unlike every other field. (For previous posts in this series, click on the Higgs folder just below the blog post title.)

It is the presence of this universal, non-zero background Higgs field that gives masses to the other elementary particles. If there were no Higgs field or its average value in the vacuum were zero, those elementary particles would have no mass and as a consequence, according to the theory of relativity, they would all travel at the speed of light in the vacuum. We can imagine how the non-zero Higgs field works using the metaphor of it being a kind of virtual syrup that permeates all of space and thus slows down the particles as they try to move through it so that they no longer travel at the speed of light. In other words, the Higgs field gives them an effective mass.

For the 18 quarks and leptons and gauge bosons, the strength of the interaction between the average vacuum value of the Higgs field V (which we said earlier has a known value 246 GeV) and the particle is directly proportional to how much mass the particle has. This will turn out to be an important fact in the detection of the Higgs particle so let me re-iterate it in the form of an equation: M=gVMV, where M is the mass of the particle and gVM is the strength of the interaction of that particle with the Higgs field. Since the masses of the particles are known, this enables us to calculate the strength of the interaction between the Higgs field and the particle.

But in particle physics reactions that involve the Higgs, we also need to know the strength of the interaction between the Higgs particle and the other 18 particles. For a quark or lepton, this turns out to have the same value M/V.

While the mass M of the W+, W, or Z particle is also given by the relationship M=gVMV, the strength of the interaction between the Higgs particle and a W+, W, or Z particle takes a slightly different form given by 2M2/V.

Since we have known the masses of all the elementary particles in the Standard Model since 1995 (except for the Higgs particle), that means we also know the strength of all the interactions between those particles and the Higgs particle.

This is vital information that is used in the production and detection of the Higgs particle. We know that the Higgs particle is unstable because its mass is much larger than other particles, and large mass particles will go into a lower energy state of smaller mass particles.

One consequence of the relationship gVM=M/V is that the Higgs particle interacts more strongly with heavier particles than light ones, which means that once a Higgs is produced it is more likely to decay into the heaviest possible particles it can. The masses of the quarks are up=2 MeV; down=5 MeV; strange=100 MeV; charm=1 GeV; bottom=4 GeV; top=172 GeV, and the masses of the charged leptons are electron=0.5 MeV; muon=106 MeV; and tau=1.78 GeV. The three electrically neutral ones (electron neutrino, muon neutrino, and tau neutrino) have almost zero masses.

Hence the Higgs is most likely to decay into particles such as the bottom quark and the tau particles, which are also very short-lived and decay into other particles. But the bottom quark, being a quark, is permanently trapped inside other particles and thus even harder to detect.

The Higgs rarely decays directly into those particles that are the easiest to detect (such as electrons and muons) because they are so light and thus only weakly interact with the Higgs particle. Also the Higgs particle does not interact directly with massless particles like the photon and the gluon. So to detect the Higgs we are forced to look for multistage processes in which the Higgs decays into heavy particles that then decay into lighter particles and so on until we get things like electrons, photons and muons that we can detect. Since we know the strength of the interaction between the Higgs and other particles, we can calculate the probability that a Higgs particle of a given mass will decay into the various channels. Since we did not know the mass of the Higgs until last July, and only knew that it likely was less than 1 TeV, the calculations had to be done for all the possible mass values, a huge computational issue.

Next: Detecting the Higgs

1. Rob Grigjanis says

Is there more to come in the series? Not sure where it could go, but the ending should be more dramatic! 🙂

2. Mano Singham says

Yes, there is a lot more to come. I forgot to put the teaser at the end.

3. Jean says

You say that the Higgs will decay into the heaviest particle it can and then say that the most likely is the bottom quark. If you assume that the Higgs is less than 1 TeV, wouldn’t the top quark be the most likely? Or are you assuming the now known Higgs mass instead of what was know at the time?

4. Rob Grigjanis says

If you assume that the Higgs is less than 1 TeV, wouldn’t the top quark be the most likely?

Less than 1 Tev and more than 344 Gev (twice the top mass of 172 Gev as it would decay to a top-antitop pair), yes. But the mass is only 125 Gev, so that is not possible.

5. Mano Singham says

Yes, there is a bit of hindsight involved in ruling out the pair production of the top quark and the anti-top quark.